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arXiv · hep-lat/9608151

Fixed versus random triangulations in 2D simplicial Regge calculus

Christian Holm·Wolfhard Janke
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Abstract

We study 2D quantum gravity on spherical topologies using the Regge calculus approach with the $dl/l$ measure. Instead of a fixed non-regular triangulation which has been used before, we study for each system size four different random triangulations, which are obtained according to the standard Voronoi-Delaunay procedure. We compare both approaches quantitatively and show that the difference in the expectation value of $R^2$ between the fixed and the random triangulation depends on the lattice size and the surface area $A$. We also try again to measure the string susceptibility exponents through a finite-size scaling Ansatz in the expectation value of an added $R^2$ interaction term in an approach where $A$ is held fixed. The string susceptibility exponent $γ_{str}'$ is shown to agree with theoretical predictions for the sphere, whereas the estimate for $γ_{str}$ appears to be too negative.

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Christian Holm, Wolfhard Janke. 1996-08-29. Fixed versus random triangulations in 2D simplicial Regge calculus. https://doi.org/10.1016/s0370-2693(96)01430-x

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